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Quadratic Formula

If S = in +...

Question

If $S = i^{n} + i^{- n}$ , where $i = \sqrt{- 1}$ and n is an integer, then the total number of possible distinct values for S is:

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more than 4

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Solution

The correct option is C 3
$s = i^{n} + i^{- n} = i^{n} + {(\frac{1}{i})}^{n} = i^{n} + i^{3 n} i f n = 4 k, s = 1 + 1 = 2 n = 4 k + 1, s = i - i = 0 n = 4 k + 2, s = - 1 - 1 = - 2 n = 4 k + 3, s = - i + i = 0$
Distinct possible values for s are -2, 0, 2.

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